{"paper":{"title":"Instance-Optimal Quantum State Certification with Entangled Measurements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.LG"],"primary_cat":"quant-ph","authors_text":"Chirag Wadhwa, Ryan O'Donnell","submitted_at":"2025-07-08T14:15:46Z","abstract_excerpt":"We consider the task of quantum state certification: given a description of a hypothesis state $\\sigma$ and multiple copies of an unknown state $\\rho$, a tester aims to determine whether the two states are equal or $\\epsilon$-far in trace distance. It is known that $\\Theta(d/\\epsilon^2)$ copies of $\\rho$ are necessary and sufficient for this task, assuming the tester can make entangled measurements over all copies [CHW07,OW15,BOW19]. However, these bounds are for a worst-case $\\sigma$, and it is not known what the optimal copy complexity is for this problem on an instance-by-instance basis. Wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.06010","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.06010/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}